Em-dash was always the wrong typographical answer, anyways:

nonbreaking-space, en-dash, nonbreaking-space: that is the right answer.

You’re trying to depict 2 things, simultaneously, through the convention: separation for the subset-of-words between the dashes, from the enclosing-sentence, AND connection, that it’s related, it’s just a subclause.

So, some do the aweful no-space/dash/no-space thing, which shows connection, but not the partial-independence…

etc.

Try different variations, & see: nonbreaking-space, en-dash, nonbreaking-space works typographically, convention/instituted-habit be damned.

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